Group #18069674 — subgroups

Subgroups — #18069674

Order 4864.

324 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926326	C₂	1	1	yes	maximal, characteristic
2	#14563668	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#338	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	—	2	1	no	—
5	C₂×#10597275	C₄	1	1	yes	characteristic
6	C₂×#10597274	C₄	1	1	yes	characteristic
7	#11926404	—	2	1	no	—
8	#11926326	—	2	1	no	—
9	#11926326	C₄	1	2	yes	complemented
10	#11926307	—	2	1	no	—
11	C₂²×M₁₆×C₁₉	—	2	1	no	—
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#338	—	2	1	no	—
14	C₁₉×#338	C₄	1	2	yes	complemented
15	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂×M₁₆×C₁₉	—	2	2	no	—
17	C₂×M₁₆×C₁₉	—	2	2	no	—
18	C₂×M₁₆×C₁₉	—	4	1	no	—
19	C₂×M₁₆×C₁₉	—	4	1	no	—
20	C₂×M₁₆×C₁₉	—	4	1	no	—
21	C₂×M₁₆×C₁₉	—	4	1	no	—
22	C₂×M₁₆×C₁₉	—	4	1	no	—
23	C₂×M₁₆×C₁₉	—	4	1	no	—
24	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
27	C₂×M₁₆×C₁₉	Q₈	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	—	2	2	no	—
29	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₂²⋊Dic₁₉	—	4	1	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	—	2	1	no	—
34	C₁₉⋊#95	—	4	1	no	—
35	#10597275	—	4	1	no	—
36	#10597274	—	4	1	no	—
37	#10597269	—	2	2	no	—
38	#10597269	—	4	1	no	—
39	C₂×C₁₉⋊C₁₆	—	4	1	no	—
40	C₂⁴×C₁₉	SD₁₆	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	—	2	1	no	—
42	C₂²×C₄×C₁₉	—	2	1	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
51	C₂²×Dic₁₉	—	4	1	no	—
52	C₂²×Dic₁₉	—	4	1	no	—
53	M₁₆×C₁₉	—	4	1	no	—
54	M₁₆×C₁₉	—	4	1	no	—
55	M₁₆×C₁₉	—	4	1	no	—
56	M₁₆×C₁₉	—	4	1	no	—
57	M₁₆×C₁₉	—	4	2	no	—
58	M₁₆×C₁₉	—	4	2	no	—
59	M₁₆×C₁₉	—	4	2	no	—
60	M₁₆×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	—	2	1	no	—
62	C₂×C₈×C₁₉	—	2	1	no	—
63	C₂×C₈×C₁₉	—	2	1	no	—
64	C₂×C₈×C₁₉	—	2	1	no	—
65	C₂×C₈×C₁₉	—	2	4	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
72	C₂²⋊Dic₁₉	—	8	2	no	—
73	C₄⋊Dic₁₉	—	4	1	no	—
74	C₄⋊Dic₁₉	—	4	1	no	—
75	C₄⋊Dic₁₉	—	4	1	no	—
76	C₄⋊Dic₁₉	—	4	1	no	—
77	C₁₉⋊C₁₆	—	4	2	no	—
78	#7255	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	—	2	1	no	—
80	C₂³×C₁₉	—	2	1	no	—
81	C₂³×C₁₉	—	4	1	no	—
82	C₂³×C₁₉	—	4	1	no	—
83	C₂³×C₁₉	#102	1	1	yes	characteristic
84	C₂³×C₁₉	#103	1	1	yes	characteristic
85	C₂³×C₁₉	#106	1	1	yes	characteristic
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	2	1	no	—
89	C₂×C₄×C₁₉	—	2	1	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#104	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
104	C₂×Dic₁₉	—	8	1	no	—
105	C₂×Dic₁₉	—	8	1	no	—
106	C₂×Dic₁₉	—	8	1	no	—
107	C₂×Dic₁₉	—	8	1	no	—
108	C₂×Dic₁₉	—	8	1	no	—
109	C₂×Dic₁₉	—	8	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	2	1	no	—
112	C₈×C₁₉	—	2	1	no	—
113	C₈×C₁₉	—	2	1	no	—
114	C₈×C₁₉	—	4	4	no	—
115	C₂×#349	—	19	1	no	—
116	#1809	—	19	1	no	—
117	C₂×#338	D₁₉	1	1	yes	characteristic
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	4	1	no	—
123	C₂²×C₁₉	—	4	1	no	—
124	C₂²×C₁₉	—	4	1	no	—
125	C₂²×C₁₉	—	4	1	no	—
126	C₂²×C₁₉	—	8	1	no	—
127	C₂²×C₁₉	#327	1	1	yes	characteristic
128	C₂²×C₁₉	#327	1	1	yes	characteristic
129	C₂²×C₁₉	#340	1	1	yes	characteristic
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	#328	1	1	yes	characteristic
133	C₄×C₁₉	#328	1	1	yes	characteristic
134	C₄×C₁₉	#339	1	1	yes	characteristic
135	C₄×C₁₉	#342	1	1	yes	characteristic
136	Dic₁₉	—	16	1	no	—
137	Dic₁₉	—	16	1	no	—
138	C₂²×M₁₆	—	2	1	no	—
139	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
140	C₂×M₃₂	—	38	1	no	—
141	C₂×#107	—	19	1	no	—
142	C₂×#106	—	19	1	no	—
143	#380	—	38	1	no	—
144	#349	—	19	2	no	—
145	#349	—	38	1	no	—
146	#340	—	38	1	no	—
147	#338	—	2	1	no	—
148	#338	Dic₁₉	1	2	yes	complemented
149	C₂×C₁₉	—	2	1	no	—
150	C₂×C₁₉	—	2	1	no	—
151	C₂×C₁₉	—	4	1	no	—
152	C₂×C₁₉	—	4	1	no	—
153	C₂×C₁₉	#1294	1	1	yes	characteristic
154	C₂×C₁₉	#1341	1	1	yes	characteristic
155	C₂×C₁₉	#1342	1	1	yes	characteristic
156	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
157	C₂×M₁₆	—	2	2	no	—
158	C₂×M₁₆	—	2	2	no	—
159	C₂×M₁₆	—	4	1	no	—
160	C₂×M₁₆	—	4	1	no	—
161	C₂×M₁₆	—	4	1	no	—
162	C₂×M₁₆	—	4	1	no	—
163	C₂×M₁₆	—	4	1	no	—
164	C₂×M₁₆	—	4	1	no	—
165	C₂×M₁₆	Dic₃₈	1	1	yes	characteristic
166	C₂×M₁₆	C₄×D₁₉	1	1	yes	characteristic
167	C₂×M₁₆	C₂×Dic₁₉	1	1	yes	characteristic
168	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
169	C₂²×C₈	—	2	2	no	—
170	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
171	C₂²×C₈	D₇₆	1	1	yes	characteristic
172	C₂×C₄⋊C₄	—	38	1	no	—
173	C₂×C₄⋊C₄	—	38	1	no	—
174	C₂×C₂²⋊C₄	—	76	1	no	—
175	M₃₂	—	38	2	no	—
176	M₃₂	—	76	1	no	—
177	C₂×C₁₆	—	76	1	no	—
178	#107	—	76	1	no	—
179	#106	—	76	1	no	—
180	#95	—	76	1	no	—
181	C₁₉	#7255	1	1	yes	characteristic, complemented, Sylow
182	C₂⁴	#64527	1	1	yes	characteristic
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	2	1	no	—
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	—	76	1	no	—
188	C₂²×C₄	—	76	1	no	—
189	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
190	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
191	C₂²×C₄	#64525	1	1	yes	characteristic
192	C₂²×C₄	#64526	1	1	yes	characteristic
193	C₂²×C₄	#64528	1	1	yes	characteristic
194	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
195	M₁₆	—	4	1	no	—
196	M₁₆	—	4	1	no	—
197	M₁₆	—	4	1	no	—
198	M₁₆	—	4	1	no	—
199	M₁₆	—	4	2	no	—
200	M₁₆	—	4	2	no	—
201	M₁₆	—	4	2	no	—
202	M₁₆	—	4	2	no	—
203	C₂×C₈	—	2	1	no	—
204	C₂×C₈	—	2	1	no	—
205	C₂×C₈	—	2	1	no	—
206	C₂×C₈	—	2	1	no	—
207	C₂×C₈	—	2	4	no	—
208	C₂×C₈	—	4	2	no	—
209	C₂×C₈	—	4	2	no	—
210	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
211	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
212	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
213	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
214	C₄⋊C₄	—	76	1	no	—
215	C₄⋊C₄	—	76	1	no	—
216	C₄⋊C₄	—	76	1	no	—
217	C₄⋊C₄	—	76	1	no	—
218	C₂²⋊C₄	—	152	2	no	—
219	C₁₆	—	76	2	no	—
220	C₂³	—	2	1	no	—
221	C₂³	—	2	1	no	—
222	C₂³	—	4	1	no	—
223	C₂³	—	4	1	no	—
224	C₂³	#10597265	1	1	yes	characteristic
225	C₂³	#10597266	1	1	yes	characteristic
226	C₂³	#10597292	1	1	yes	characteristic
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	152	1	no	—
238	C₂×C₄	—	152	1	no	—
239	C₂×C₄	—	152	1	no	—
240	C₂×C₄	—	152	1	no	—
241	C₂×C₄	—	152	1	no	—
242	C₂×C₄	—	152	1	no	—
243	C₂×C₄	#10597262	1	1	yes	characteristic
244	C₂×C₄	#10597262	1	1	yes	characteristic
245	C₂×C₄	#10597263	1	1	yes	characteristic
246	C₂×C₄	#10597263	1	1	yes	characteristic
247	C₂×C₄	#10597264	1	1	yes	characteristic
248	C₂×C₄	#10597267	1	1	yes	characteristic
249	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
250	C₂×C₄	#10597289	1	1	yes	characteristic
251	C₈	—	2	1	no	—
252	C₈	—	2	1	no	—
253	C₈	—	2	1	no	—
254	C₈	—	2	1	no	—
255	C₈	—	4	4	no	—
256	C₂²	—	2	1	no	—
257	C₂²	—	2	1	no	—
258	C₂²	—	2	1	no	—
259	C₂²	—	2	1	no	—
260	C₂²	—	4	1	no	—
261	C₂²	—	4	1	no	—
262	C₂²	—	4	1	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	8	1	no	—
265	C₂²	#11926277	1	1	yes	characteristic
266	C₂²	#11926277	1	1	yes	characteristic
267	C₂²	#11926306	1	1	yes	characteristic
268	C₄	—	2	1	no	—
269	C₄	—	2	1	no	—
270	C₄	—	304	1	no	—
271	C₄	—	304	1	no	—
272	C₄	#11926280	1	1	yes	characteristic
273	C₄	#11926280	1	1	yes	characteristic
274	C₄	#11926304	1	1	yes	characteristic
275	C₄	#11926310	1	1	yes	characteristic
276	C₂	—	2	1	no	—
277	C₂	—	2	1	no	—
278	C₂	—	4	1	no	—
279	C₂	—	4	1	no	—
280	C₂	#14561514	1	1	yes	characteristic
281	C₂	#14561625	1	1	yes	characteristic
282	C₂	#14561628	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926326

C₂

yes

maximal, characteristic

#14563668

C₂

yes

maximal, characteristic

C₂×C₁₉×#338

C₂

yes

maximal, characteristic

C₂×#10597269

—

C₂×#10597275

C₄

yes

characteristic

C₂×#10597274

C₄

yes

—

—

C₄

yes

complemented

#11926307

—

C₂²×M₁₆×C₁₉

—

C₂²×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#338

—

C₁₉×#338

C₄

yes

complemented

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₁₉⋊#95

—

—

—

—

—

C₂×C₁₉⋊C₁₆

—

C₂⁴×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₁₉⋊C₁₆

—

#7255

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

100

C₂×C₄×C₁₉

#103

yes

characteristic

101

C₂×C₄×C₁₉

#104

yes

characteristic

102

C₂×C₄×C₁₉

#104

yes

characteristic

103

C₂×C₄×C₁₉

#107

yes

characteristic

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

C₂×Dic₁₉

—

108

C₂×Dic₁₉

—

109

C₂×Dic₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₈×C₁₉

—

113

C₈×C₁₉

—

114

C₈×C₁₉

—

115

C₂×#349

—

116

#1809

—

117

C₂×#338

D₁₉

yes

characteristic

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

#327

yes

characteristic

128

C₂²×C₁₉

#327

yes

characteristic

129

C₂²×C₁₉

#340

yes

characteristic

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

#328

yes

characteristic

133

C₄×C₁₉

#328

yes

characteristic

134

C₄×C₁₉

#339

yes

characteristic

135

C₄×C₁₉

#342

yes

characteristic

136

Dic₁₉

—

137

Dic₁₉

—

138

C₂²×M₁₆

—

139

C₂²×M₁₆

C₂×D₁₉

yes

characteristic

140

C₂×M₃₂

—

141

C₂×#107

—

142

C₂×#106

—

143

#380

—

144

#349

—

145

#349

—

146

#340

—

147

#338

—

148

#338

Dic₁₉

yes

complemented

149

C₂×C₁₉

—

150

C₂×C₁₉

—

151

C₂×C₁₉

—

152

C₂×C₁₉

—

153

C₂×C₁₉

#1294

yes

characteristic

154

C₂×C₁₉

#1341

yes

characteristic

155

C₂×C₁₉

#1342

yes

characteristic

156

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

157

C₂×M₁₆

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂×M₁₆

—

161

C₂×M₁₆

—

162

C₂×M₁₆

—

163

C₂×M₁₆

—

164

C₂×M₁₆

—

165

C₂×M₁₆

Dic₃₈

yes

characteristic

166

C₂×M₁₆

C₄×D₁₉

yes

characteristic

167

C₂×M₁₆

C₂×Dic₁₉

yes

characteristic

168

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

169

C₂²×C₈

—

170

C₂²×C₈

C₄×D₁₉

yes

characteristic

171

C₂²×C₈

D₇₆

yes

characteristic

172

C₂×C₄⋊C₄

—

173

C₂×C₄⋊C₄

—

174

C₂×C₂²⋊C₄

—

175

M₃₂

—

176

M₃₂

—

177

C₂×C₁₆

—

178

#107

—

179

#106

—

180

#95

—

181

C₁₉

#7255

yes

characteristic, complemented, Sylow

182

C₂⁴

#64527

yes

characteristic

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

190

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

191

C₂²×C₄

#64525

yes

characteristic

192

C₂²×C₄

#64526

yes

characteristic

193

C₂²×C₄

#64528

yes

characteristic

194

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

195

M₁₆

—

196

M₁₆

—

197

M₁₆

—

198

M₁₆

—

199

M₁₆

—

200

M₁₆

—

201

M₁₆

—

202

M₁₆

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

C₄×Dic₁₉

yes

characteristic

211

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

212

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

213

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₂²⋊C₄

—

152

—

219

C₁₆

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

#10597265

yes

characteristic

225

C₂³

#10597266

yes

characteristic

226

C₂³

#10597292

yes

characteristic

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

152

—

238

C₂×C₄

—

152

—

239

C₂×C₄

—

152

—

240

C₂×C₄

—

152

—

241

C₂×C₄

—

152

—

242

C₂×C₄

—

152

—

243

C₂×C₄

#10597262

yes

characteristic

244

C₂×C₄

#10597262

yes

characteristic

245

C₂×C₄

#10597263

yes

characteristic

246

C₂×C₄

#10597263

yes

characteristic

247

C₂×C₄

#10597264

yes

characteristic

248

C₂×C₄

#10597267

yes

characteristic

249

C₂×C₄

C₁₉⋊#95

yes

characteristic

250

C₂×C₄

#10597289

yes

characteristic

251

C₈

—

252

C₈

—

253

C₈

—

254

C₈

—

255

C₈

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

#11926277

yes

characteristic

266

C₂²

#11926277

yes

characteristic

267

C₂²

#11926306

yes

characteristic

268

C₄

—

269

C₄

—

270

C₄

—

304

—

271

C₄

—

304

—

272

C₄

#11926280

yes

characteristic

273

C₄

#11926280

yes

characteristic

274

C₄

#11926304

yes

characteristic

275

C₄

#11926310

yes

characteristic

276

C₂

—

277

C₂

—

278

C₂

—

279

C₂

—

280

C₂

#14561514

yes

characteristic

281

C₂

#14561625

yes

characteristic

282

C₂

#14561628

yes

characteristic

	subgroup	G/H
center	C₂²	#11926277
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂²×M₁₆	C₂×D₁₉
Fitting	C₂×C₁₉×#338	C₂
socle	C₂²×C₁₉	#327
prime radical	C₂⁴×C₁₉	SD₁₆
cosocle	C₂²×M₁₆×C₁₉	C₂²
hypercenter	C₂×#338	D₁₉
hypocenter	C₁₉	#7255
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#338

subgroup

G/H

center

C₂²

#11926277

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₂²×M₁₆

C₂×D₁₉

Fitting

C₂×C₁₉×#338

C₂

socle

C₂²×C₁₉

#327

prime radical

C₂⁴×C₁₉

SD₁₆

cosocle

C₂²×M₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#338

N	H ≅ G/N	type
9. #11926326	C₄	semidirect
14. C₁₉×#338	C₄	semidirect
148. #338	Dic₁₉	semidirect
181. C₁₉	#7255	semidirect

H ≅ G/N

type

9. #11926326

C₄

semidirect

14. C₁₉×#338

C₄

semidirect

148. #338

Dic₁₉

semidirect

181. C₁₉

#7255

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11926326	2
#14563668	2
C₂×C₁₉×#338	2
#7255	19

subgroup

index

C₂×#11926326

#14563668

C₂×C₁₉×#338

#7255

Subgroups — #18069674

Conjugacy classes of subgroups

Complements

Maximal subgroups